A theory of the time dependence of resonance transfer of excitation energy between molecules is developed in terms of memory functions appearing in the transition rates of a generalized master equation (GME). The memory can be computed explicitly and, due to the coarse-graining operation incorporated in our derivation of the GME, the accuracy of the memory function depends only on the amount of detailed information one has, or wishes to include, about the spectrum and dynamics of the system. The formalism yields a unified description of coherent motion at short times and diffusive transport at long times, and for the case of transfer between and among identical molecules provides a generalized approach to the theory of exciton transport. Memory functions for transfer between anthracene molecules are obtained as an illustration of the theory. The connection between the new formalism and existing exciton-transport theories is indicated and its relation to the theory of non-Markoffian random walks is presented.

• Received 11 February 1974

DOI:https://doi.org/10.1103/PhysRevB.9.5279